This puzzle is about a square-headed architect who is designing a museum in the shape of an nxnxh square box, where n is an integer denoting the side length and h is the height of the building.(adsbygoogle = window.adsbygoogle || []).push({});

Building design is subject to the following additional constraints:

1. For any n chosen there will be exactly n rooms.

2. All rooms will have the same area n, in order to be able to hold similar crowd sizes.

3. All rooms will have the same perimeter so that they all have equal total wall areas.

4. All rooms will have the same number of neighboring rooms so as to be equivalent for the purpose of moving around the building.

Note: Two rooms are neighbors if they share at least a part of a wall, not just a corner.

QUESTIONS:

1. Simple solutions can be found for n=1,2,3 and 4. Can you check this?

2. No solutions are known for n=5. Are there any?

3. Two solutions are known for n=6. Can you find them? Are there more?

4. Are there solutions for n>6? Can we help the architect find interesting (i.e., large n) designs?

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# Square-headed Architect Riddle

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